Problem: Simplify the following expression: $x = \dfrac{1}{3y} + \dfrac{1}{5y}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $3y$ and $5y$ $\lcm(3y, 5y) = 15y$ $ x = \dfrac{5}{5} \cdot \dfrac{1}{3y} + \dfrac{3}{3} \cdot \dfrac{1}{5y} $ $x = \dfrac{5}{15y} + \dfrac{3}{15y}$ $x = \dfrac{5 +3}{15y}$ $x = \dfrac{8}{15y}$